On 10/20/2012 08:41 PM, Adam wrote:
> On 20.10.2012 21:00, Jaime Villate wrote:
>> On 10/20/2012 10:55 AM, Adam wrote:
>>> Here are good images
>>> http://www.clarku.edu/~djoyce/complex/powers.html
>>> http://facstaff.unca.edu/mcmcclur/Mathematica/ComplexDynamics/HTMLLinks/ComplexQuadAndCubicIteration_1.html
>>>
>>>
>>>
>>> The problem is that vector draws a straight line, but I need a curve (
>>> complex square is a rotation ).
>>>
>>> I'm working to get better result.
>>> Any help is welcome.
>> Hi Adam,
>> If your objective is just to draw the first figure in that reference,
>> with the arrows, it can be done using plotdf (see the attached figure).
>> If your objective is something else, please remind us.
>> Cheers,
>> Jaime
> Wow, that's it !
>
> How did you do it ?
I used a dynamical system that I know it has a circular repulsive limit
cycle:
dx/dt = -y+x*(x^2+y^2-1)
dy/dt = x+y*(x^2+y^2-1)
(%i1) dx: -y+x*(x^2+y^2-1)$
(%i2) dy: x+y*(x^2+y^2-1)$
(%i3) plotdf([dx,dy],[x,-2,2],[y,-2,2],[vectors,""],[trajectory_at,0,1]);
That will show you only the limit cycle (currently plotdf accepts only
one "trajectory_at"). I then did the blue and green trajectories by hand:
* Click on the tools icon in plotdf's menu
* Change the fieldlines color to blue (or gray or whatever)
* Change nsteps to 50.
* Click on OK and then click on some points inside the circle.
I may then change the fieldlines color again and click on some points
outside of the circle. When you are happy with the plot, click on the
disk-drive icon and save your plot in Postscript format.
Regards,
Jaime (who wishes he had some free time to translate his books
http://def.fe.up.pt into English)